My older brother who had never shot, got curious after her went shooting with me and he fired my XD 9 sub compact, then shot my AR. He's now the pround owner of a couple handguns, most recently an M&P Shield. He also now shoots better then I do when it comes to handguns.
I have always introduced young children and newbes to firearms, after teaching them (and demonstrating) safety use of firearms using a 22 rifle off a bench at a target fairly close (25 to 50 foot). This allows them to 1) Fire a gun with virtually no recoil and 2) usually hit the target fairly well.
When they become comfortable with the 22 rifle, then move up to a 22 handgun like my semi-auto Ruger. Again almost no perceived recoil and a good chance to hit a target at 20 foot or so.
Then I explain that larger calibers will make a LOT more noise and recoil will hurt your shoulder or hand if you don't handle the firearm correctly. After that I introduce them to either a higher power rifle (AK - AR style or bolt 243 etc.) and move up to high power (up to my 30-06's) when/IF THEY desire. Same with handgun - move up in caliber, "Blast noise" and recoil gradually as THEY desire. 45 Acp, clear up to my 44 mag.
I think too many people forget how they started out and don't remember the "shock" the first time they fired a Magnum handgun or high power rifle. The last thing I want to do is "scare" or make a person "hurt from recoil" and decide that shooting is not for them!
The best luck I've had converting some "I hate Guns" people was with a Model 60 Marlin .22Lr with a four powers scope. Any semi auto rifle in .22 with a scope will do. I start them off shooting from a bench rest at about 25yrds with plenty of reactive targets on the backstop (dirt mound in this case), like Clay Pigeons, pop cans, and even Tennis balls. (check your range rules) If the newbe insist on trying a handgun, I've found that a Ruger MkII or something like that works pretty well providing they have comfortable ear protection. My general observation is... a new shooter no matter what age doesn't like loud report, and doesn't like recoil... But LOVES to see something move, or break when they hit it. For the really shy first timer sometimes an Air Rifle/Pistol is the best way to go.
M134 Minigun. Hands down. If you don't have a love for firearms after dropping the hammer on one of these you have no soul, or you're a hippie. Either way, same thing.
A water gun who doesn't love a good ole water gun fight......... oh wait not that type of gun. An M16 anyone who's never fried a firearm before and joins the service is sure to get a pleasant experience with any firearm they can get training on.
I have started several people on .22's but the guns that have really turned people's lights on are the 1911 in .45 and the 5.56 AR15.
When people who do not know firearms shoot those it clicks that these are real deal big boy guns. These are the things action movie heroes shoot and my new shooter is totally capable of shooting the guns the big boys shoot.
Take someone who is afraid of guns and teach them to shoot the .22. That is a hell of an accomplishment and you have done them a great service. Take that same shooter and after teaching them to shoot the .22 at 25 yards, put them on an AR at 100, 200 yards and let them ring the steel for a mag, that proves the concept of their learning and puts them in love with shooting. I have seen it happen. It is pure awesome.
I forget the model number but a S&W k frame in .22 with a 6in full underlug barrel.
Also turned many people into believers with a lightweight 10/22 with a red dot.
Also bench shooting a heavy rifle in a light recoil caliber can be fun and its nice to show people that its not that hard to hit targets at 200-300 yards